Obviously this only applies to AC-heated filaments, although some noise from a regulated DC supply could be transferred. In the case of overall noise figure, a magnetized cathode could cause a greater randomization of shot noise, thus increasing RMS values.

Exactly.
While I've said it before, on simple IDHTs it's pretty easy to actually measure and listen to the coupling effect of cathode to heater and vice versa.
Snubbing across heater pins can be effective in reducing this effect, demagnetizing the tube helps as well.

my 2 cents...back in the good old days of de-maging big ol' 16 & 24 track headstacks we were always taught to keep the demagnetizer rotating as we pulled it away from the head. BTW, about 20% of the time we managed to magnetize the head rather than de-mag it and this procedure was always seen as a fix of last resort! In other words, be careful.